Talmudology Redux - Readers Suggest How Rabban Gamliel Did It…

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The Story So Far…

Last time on Talmudology we discussed the mysterious tube that Rabban Gamliel used to estimate the distance of his ship from the shore, described on Eruvin 43b. The tube was likely some kind of protractor which measured the angles between two objects. But how this enabled the calculation of distance was not explained, and trigonometry had not yet been invented. We concluded that it was a mystery.

“And so the question of how Rabban Gamliel calculated the distance to the shore on that eve of Shabbat must remain a mystery.”

Talmudology Readers to the Rescue

But Talmudology readers don’t like to leave things a mystery. Several wrote in with various solutions, and with their permission we are sharing them with you.

Jeffrey Lubin suggested that the answer might be something to do with making some markings on the glass at the end of the tube (assuming of course that it did indeed contain glass).

If he was familiar with the height of the towers (per the Yerushalmi); Is it possible that he was able to place upper and lower markings (with grease or etches or something else) on the glass at the end of his tube, and if the entire towers fell within those markings he was still too far out and once the towers reached the full distance between the markings he knew he was within 2000 amot?

This same device could be useful if he was on land or on sea and since he knew the heights of the towers, he had likely been to the area before. Perhaps he traveled there regularly. It’s easier than measuring angles and doing complex mathematical calculations in the moments before shabbat came in. (He may even have had multiple Glass attachments for different ports - with the markings in different places on the glass)

Another suggestion was made by Ori Pomorantz:

He [Rabban Gamliel] didn't need a general solution to measure distances. He just needed to know whether the distance is above or below 2000 cubits. On a weekday he could have gone 2000 cubits from the tower and measured the angle the tower appeared to be. Then, Friday afternoon, he could have checked against that particular angle. If the tower appears as a bigger angle, they're within Tchum Shabbat. If it appears smaller, they aren't. 

Shalom Kelman suggested that the key lies with similar triangles.

The ancients were certainly familiar with this area of mathematics. They might not have had tangent tables but using proportions would have been sufficient for the task at hand. See the Hebrew Art Scroll for a worked-out example. So if Rabban Gamliel could measure an angle from his sextant to a tower of known height, the calculation should be straight forward. 

Here is the original note to which Shalom referred in the ArtScroll Hebrew Talmud, together with a free translation. It too relies on a prior measurement of 2,000 amot and securing the tube and the angle subtended when viewing that precise distance.

We are discussing a tube attached to the top of a pillar, which is pointing downwards and aligned so that a person looking through it will see a distance of 2,000 amot. This distance is [previously] determined by placing the pillar on flat terrain, measuring out 2,000 amot, and placing an object at that distance. Then the observer points the tube down towards the object until it can be seen through the tube.

With the tube at that angle, a triangle is formed between the pillar, the ground and the hypotenuse, which is the line of sight from the tube to the ground. Then the distance from the base of the pillar to where the line of sight meets the ground must be 2,000 amot. When a person looks through the tube his line of sight is along the hypotenuse and where it meets the ground must be a distance of 2,000 amot from where he is standing, which is the limit of where he may walk on Shabbat.

Marvin Littman, another Talmudology reader, seems to have a very good memory. He sent us a paper published in the American Journal of Ophthalmology, which he chanced upon when he was in a university library “some time in the 1970s.” The paper, A Telemeter without Refractive Optics came from the Vision Research Laboratory at Hadassah University Hospital. It is based on “nonconcentric overlapping monocular fields”, and the author claims that Rabban Gamliel’s tube used this method to measure distances, making it “the earliest telemeter in the world.” Here is the brief paper, for your delight and consideration:

And finally, Avi Grossman wrote to inform us that “even without the fancy calculations and knowledge of tangents, anyone can calculate the distance using some drawn-to-scale sketches and a given angle and length.”

Avi referred us to the American cartoonist Carl Barks (1901-2000), who created and drew the first Donald Duck stories. In one of these stories, Donald Duck, Huey, Dewey and Louie Duck, known as the Junior Woodchucks, face off against the all-female Chickadee Patrol. You can read the full story here, but the bit that suggests an answer to how Rabban Gamliel calculated his distance from the shore is reproduced below:

In the end, the Woodchucks use a different method to build their bridge, and (spoiler alert) both teams tie. Might Rabban Gamliel have used a similar method to calculate his distance from the shore? And are there any other examples of a passage of Talmud being elucidated by a Donald Duck cartoon?

There are, to be sure problems with each method; for example, there is no suggestion in the Talmud that Rabban Gamliel had done any prior calculations, or even that he knew the geography of the port into which he sailed that Friday evening (although the Yerushalmi’s note the he knew the height of the towers might suggest a familiarity with the area). But the fact we received these different solutions is a testament to the Talmudology readership. And a reminder that the work of explaining the Talmud does not end with Rashi and the other famous commentaries. It is an ongoing process, and sometimes even involves cartoon ducks.

Eruvin 43b ~ Rabban Gamliel's Trigonometry

Last time on Talmudology we tried to determine the nature of the special tube that Rabban Gamliel carried with him on a boat, and which allowed him to calculate its distance from the shore. Here is a recap:

עירובין מג, ב

פעם אחת לא נכנסו לנמל עד שחשיכה אמרו לו לרבן גמליאל מה אנו לירד? אמר להם מותרים אתם שכבר הייתי מסתכל והיינו בתוך התחום עד שלא חשיכה

Once a ship did not enter the port until after nightfall on Shabbat eve. The passengers asked Rabban Gamliel, “what is the halakha with regard to alighting from the boat at this time? [In other words, were we already within the city’s limit before Shabbat commenced?] 

He said to them: You are permitted to alight, as I was watching, and I observed that we were already within the city’s limit before nightfall. [The port is therefore within the area on which we may walk on Shabbat.]

Regardless of whether it was a telescope (unlikely) or a protractor of some kind (more likely, but still not certain), the question we will address today is how Rabban Gamliel used the instrument to determine his distance from the shore.

The Jerusalem Talmud Comes to the Rescue

There is nothing in the Babylonian Talmud that would suggest an answer. But the Jerusalem Talmud goes into a little more detail, and in so doing it provides us with an explanation:

תלמוד ירושלמי עירובין כח, ב

מצודות היו לו לרבן גמליאל שהיה משער בה עיניו במישר

Rabban Gamliel knew of the heights of some towers (along the coast) which he estimated with his eyes…

You can only use the trigonometry of a right-angled triangle if you know the length of one of the sides of the triangle, and one of its angles. The Yerushalmi provides the key. Rabban Gamliel knew the height of the towers that he was observing (AB in the diagram below). Here is the explanation provided by W.M. Feldman in his classic work Rabbinical Mathematics and Astronomy, first published in London in 1931.

Did the Rabbis of the Talmud know their trigonometry?

So Rabban Gamliel could have used some high-school math to determine his distance from the shore, if he knew the height of the tower (AB) the angle (ACB), and the tan of that angle. So were sines, cosines and tangents known to the talmudic world?

I had no idea. But I asked a friend who is an Associate Professor of Writing and of Mathematics at The George Washington University in Washington DC. He pointed me to this book on the history of mathematics, and made the following observations.

Based on a quick perusal of Boyer's A History of Mathematics, the notions of trigonometric ratios were well known to Aristarchus (and hence, presumably, to Archimedes). Aristarchus was doing more complex calculations than for right-angled triangles; it seems likely that he understood the right-angle case, although I didn't see explicit mention of that.  Also, the Babylonians at the same time had active astronomical investigations going on, and were known to use ratios of sides of triangles in relation to angles.

However, no one had a notion of trigonometric function for more than 1800 years after that. Trigonometric ratios were just that - individual numerical ratios. This was one of the hang-ups that Newton and Leibnitz almost, but didn't quite, work through. Trigonometric results were known, but they weren't necessarily expressed, or interpreted, in the same way as we now do. So, Rabban Gamliel might not have been calculating tan(x), per se…

However, I think it's safe to say that if R"G did a calculation, it didn't look anything like what the book shows. First, there was no "tan" function. Second, fractions hadn't been invented. Third, decimal expansions hadn't been invented. Fourth, calculation of the tangent of that angle would have required a careful and explicit approximation process, and could not have been done so handily.

Which means that while Feldman’s math is correct, it wasn't the math used by Rabban Gamliel. And so the question of how Rabban Gamliel calculated the distance to the shore on that eve of Shabbat must remain a mystery.

Eruvin 43b ~ Jews and their Telescopes

The chapter we are currently studying deals with the prohibition of traveling more than 2,000 amot (about 3,600 feet or just over a kilometer) in any direction on Shabbat unless an eruv, a legal boundary, had been built. Now what happens if you are on a ship that docks on Friday night, after Shabbat has begun? May you disembark? If the ship was within 2,000 amot of the port then you may leave, but if it was a greater distance than this you must remain on the boat until the end of Shabbat.

The Mishnah relates an incident when this question arose. Rabban Gamliel came to the rescue, and announced that he had determined that the ship was indeed within 2,000 amot of the port prior to the beginning of Shabbat.

ערובין מא, א

פעם אחת לא נכנסו לנמל עד שחשיכה אמרו לו לרבן גמליאל מה אנו לירד? אמר להם מותרים אתם שכבר הייתי מסתכל והיינו בתוך התחום עד שלא חשיכה

Once a ship did not enter the port until after nightfall on Shabbat eve. The passengers asked Rabban Gamliel, “what is the halakha with regard to alighting from the boat at this time? [In other words, were we already within the city’s limit before Shabbat commenced?] 

He said to them: You are permitted to alight, as I was watching, and I observed that we were already within the city’s limit before nightfall. [The port is therefore within the area on which we may walk on Shabbat.]

But how exactly did Rabban Gamliel know this? The Mishnah is silent on the issue, but the Talmud fills in some details.

ערובין מג,ב

תנא שפופרת היתה לו לרבן גמליאל שהיה מביט וצופה בה אלפים אמה ביבשה וכנגדה אלפים בים 

Rabban Gamliel had a special tube through which he would look and see a distance of two thousand cubits on land, and also determine a corresponding distance of two thousand cubits at sea.

Sidebar - which Rabban Gamliel was it?

There are several people in the Talmud who used the title of Rabban Gamliel. Given the context of the Mishnah, the one we are talking about here is Rabban Gamliel of Yavneh, also known as Rabban Gamliel the Second, the one who led the Sanhedrin immediately after the destruction of Jerusalem in 70 C.E.

And this is not the only time Rabban Gamliel was on a ship with Rabbi Yehoshua, Rabbi Akiva and others. In the tractate Horayot (10a) we read that Rabban Gamliel and Rabbi Yehoshua were sailing together when the latter demonstrated his navigational skills which involved a comet known today as Halley’s Comet. (You can read all about that here.) Rabban Gamliel seemed to know nothing of this comet, and yet here he is described as owning an instrument that allowed the precise measurement of distances. Perhaps Rabban Gamliel’s interests were only terrestrial.

“Rabban Gamliel’s tube is “one of the most puzzling scientific passages in the Talmud.””

Rabban Gamliel’s measuring device - according to Rashi

What then, was the nature of this special tube? According to the medieval exegete Rashi, who lived over one thousand years after Rabban Gamliel, the tube worked like this:

שפופרת.קנה חלול וכשהוא ארוך אין צופין בו למרחוק וכשהוא קצר צופין בו יותר והיתה שפופרת של רבן גמליאל מתוקנת למדת צפיית אלפים או בים או ביבשה

A tube: It was a hollow tube that when it is long you cannot see far though it and when it is short you can see farther. The tube of Rabban Gamliel was calibrated to measure 2,000 amot whether on land or sea.

That sounds rather like a simple telescope in which the focal length may be changed. However, telescopes which use lenses to focus were invented (at least in Europe) only around 1608. We do not know the name of the inventor, though in October of that year a Dutchman by the name of Hans Lipperhey had submitted a patent for a telescope. Did Rabban Gamliel really use a telescope over 1,500 years prior to this patent?

The Koren English Talmud suggests in a note that the tube was “a kind of precise protractor, similar to those used for astronomical measurements, i.e a type of sextant, the early form of which is known as an astrolabe.” The ArtScroll Schottenstein Talmud notes that Rabban Gamliel’s tube “operated without lenses, which were not invented until some fourteen centuries later.” It is challenging to figure out what exactly this tube was.

The Problem with Rashi

The mathematician and President of the Hebrew University of Jerusalem Selig Brodetsky (1888-1954) wrote a lengthy essay titled Astronomy in the Babylonian Talmud, which was published in English in 1979. Brodetsky calls the description of Rabban Gamliel’s tube “one of the most puzzling scientific passage in the Talmud.” And he describes Rashi’s interpretation as “even more puzzling.”

Rashi’s explanation can point to nothing else than a telescope. Are we then, to conclude that the Rabbis invented such an instrument fifteen centuries before European scientists became aware of its construction and capabilities? Or shall we baldly assert that someone has tampered with Rashi, and substituted an explanation in terms of instruments known to modern science? The second alternative is even more difficult to accept than the first, for no other reading of the Rashi is known.

The Astrolabe

In his Commentary on the Mishnah, Maimonides explained the the tube used by Rabban Gamliel was an astrolabe:

שמסתכלין בו החוזים בכוכבים ונקרא בערבי אצטרל"ב ואיני רוצה להאריך ולהזכיר איך יושג כי זה הדבר בזה הענין ארוך ואפילו באריכות לא יבין זה אלא מי שידע בחכמת התשבורת

…It was the device used by astronomers and known in Arabic as an “astrolabe.” I do not want to go into lengthy details and describe how it is used, because it is a lengthy process. And even then only those who are especially knowledgabe will understand

The astrolabe described here is a device that is used to measure the angular distance between stars or planets. As we have seen, this is the explanation offered in the Koren English Talmud. So according to Maimonides the tube did not provide any magnification.

The Nimrud Lens

The Nimrud Lens on display at The British Museum in London. It is 38 mm (1.5 in) in diameter and 23 mm (0.9 in) thick. And it is 3,000 years old

Brodetsky wondered how Rabban Gamliel could have used a telescope with lenses so long before it was “invented” in Europe. What he didn’t mention was that there is some controversial evidence that lenses were used millennia ago. The Nimrud Lens, discovered in Iraq in 1850, is a piece of crystal about 3,000 years old that appears to have been used to focus the rays of the sun, and perhaps even as a magnifying glass. Its function is however, a matter of academic dispute. Some have suggested that it was part of an ancient telescope. A curator at the The British Museum, where the lens is displayed, disagreed disagreed:

When it was found by Layard this oval piece of ground quartz or rock crystal was immediately identified as a lens, and it has come to be known as the 'Nimrud lens'. It could certainly have been used as a crude magnifying glass, with a focal length of 12 centimetres from the plane surface. Over the years it has been examined by a number of opticians, many of whom believe that it was deliberately manufactured as a lens. However, although this piece of rock crystal has been carefully ground and polished, and undoubtedly has optical properties, these are probably accidental. There is no evidence that the Assyrians used lenses, either for magnification or for making fire, and it is much more likely that this is a piece of inlay, perhaps for furniture. This is supported by Layard's statement that this object 'was buried beneath a heap of fragments of beautiful blue opaque glass, apparently the enamel of some object in ivory or wood, which had perished

Whether or not the glass was merely decorative or was used to magnify will never be known. But it raises at least the possibility that people were using lenses long before the time of Galileo.

Benjamin of tudela and the Mirror of Alexandria

Benjamin of Tudela (1130-1173) was a traveller who visited Africa and Asia, and wrote about his adventures in his Sefer Hamasaot (The Book of Travels). In the port city of Alexandria he described a tower or lighthouse, on the top of which

…there is a glass mirror. Any ships that attempted to attack or molest the city, coming from Greece or from the Western lands, could be seen by means of this mirror of glass at a distance of twenty days' journey, and the inhabitants could thereupon put themselves on their guard.

This is certainly not a telescope, but just what this mirror did (and how it did it) is not clear. Other texts mention this famous mirror, and many of them build on the description given by Benjamin. Now let’s jump forward by four-hundred years.

Azariah Figo on the Message of the telescope

Azariah Figo (1579-1647) was a rabbi who served in both Pisa and Venice during the era of the Italian ghetto. A year after his death his sermons were published in a work titled Binah Le’ittim, and since then they have been reprinted some fifty times. In a sermon delivered on Rosh Hashanah that happened to fall on Shabbat (like it does this year) he reminded his congregation about the wondrous ability of human creativity.

Azariah Figo. Binah Le’ittim. Benai Berak. Mishor 1994. p54. (In the original but less legible 1648 edition it appears on page 24b.)

The human being was given intelligence by the Source of all Wisdom and was given great strength…until He filled his heart on numerous occasions with the capacity to make artificial inventions which replicate that which is found in nature. Because of his weakness of matter or the deficiency in its preparation…man tries to correct and replace it by some discovery or invention drawn from his intelligence to the point where he will overcome what he naturally lacked.

We have seen people with poor sight, who because of a deficiency cannot see with their eyes things that are far away or even that which is close. But human intelligence was able to invent reading glasses that are placed on the bridge of the nose in front of the eyes. This improves their vision either a little or a lot, depending on the circumstances.

This was the case for the hollow tube of Rabban Gamliel, cited in the fourth chapter of Eruvin (43b), who said “I have already seen through it and I can verify that we are inside the boundary for Shabbat.

Figo was not giving a lesson in the history of science. Rather he was relating a spiritual parable, appropriate for Rosh Hashanah, the very day on which the sermon was delivered. Figo explained that just as we are able to make up for our physical deficiencies with eyeglasses and Rabban Gamliel’s tube, so too are we able to make up for our spiritual deficiencies with objects such as the shofar (the ram’s horn blown on Rosh Hashanah,) or the tzitizt, (fringes placed on the corners of a garment). Here is how the historian David Ruderman summarized the sermon:

Figo…was teaching his Jewish message by appealing directly to the immediate cultural context of his listeners. He was not teaching contemporary science to his coreligionists; he rather assumed that this knowledge was a commonplace in their experience with the world around them. As any wise preacher would do, Figo appropriated that experience to make his point about the religious message of the Jewish holiday.

And so the telescope became a scientific instrument that taught a religious lesson on Rosh Hashanah, the Jewish New Year, which we will celebrate again in two days.

Leon of Modena on the Telescope

Leon of Modena (1571-1648) was a contemporary of Azariah Figo and like him also served as a rabbi in Venice. Modena wrote at least a dozen books, including a commentary on the Ein Yaakov, which he called Haboneh (The Builder). In that commentary, Modena claimed that “there is nothing new under the sun” and that the telescopes of his day had been preceded by Rabban Gamliel’s tube.

“There is nothing new under the sun (Ecclesiastes 1:9).” The telescope which contains a few pieces of glass and which can be found today allows one to look many miles into the distance on land and at sea. It is wondrous to behold. And it had already been invented and used by Rabban Gamliel using his wide knowledge, which was greater than all his contemporaries…

Leon, like his contemporary, was also using the telescope to make a spiritual point. Modern inventions were predated by the Jewish sages, whose scientific knowledge eclipsed that of future generation (וגם חקרו רבן גמליאל בחכמתו הרהבח אשר גדל על כל באלה בתכונה).

ABraham Yagel on the Telescope

Abraham ben Hananiah Yagel was born in Italy in 1553. Although he was more interested in medicine than astronomy, he wrote several works that contain discussions of various astronomical phenomena. In his unpublished work Be’er Sheva he addresses both Galileo’s discoveries and the invention of the telescope (Ms. Oxford-Bodi. 1306: Be'er Sheva, Chap. 15, fols. 48a-53b). Here is what Yagel wrote about the new astronomy revealed by Galileo.

Our words were sincere, that in every generation things will be revealed to humanity which never were imagined by the ancients ... for behold you have seen among the fruits of the earth and the animals of the forest what we wrote in previous chapters of our composition, and also now in this chapter you shall truly see that my witness that is in heaven and my work that is on high will appear regarding the words of a wise Gentile man who in our day found several stars from the nebula which the ancients never saw and he placed their signs and their markings in a book and also spoke of the appearances seen on the moon and not in puzzles but the true opinion and what are the analogous figures to the human face [seen] from above ....

Yagel found two precursors in Jewish history that suggested the telescope’s invention long preceded Galileo. The first was Rabban Gamliel’s tube mentioned on today’s page of Talmud. The second is described again, by historian David Ruderman.

…he discovered in the tenth­ century commentary of the Sefer Yetsirah of the Italian Jewish doctor, Shab­betai Donnolo. In the introduction to this work, Donnolo describes his teacher in astronomy, an Arab named Bagdash. whose teaching agreed with that of the ancients and the Jews, especially the Baraita de-Samuel, and who taught him how to use an instrument which Yagel considered to be the same as Galileo's spyglass. "And thus this secret of the instrument in which the paths of heaven are seen was covered up, for our forefathers never imagined it and now it has been revealed, for there is nothing new under the sun."

Once again, the message is that the rabbis of the talmud had previously invented the telescope, long before it began to be used in Europe.

Delmedigo looks through Galileo’s Telescope

In the annals of Jews and telescopes one of the most remarkable stories is the relationship between Joseph Delmedio of Candia and his teacher Galileo. (Yes, that Galileo.) I have written about it in detail elsewhere, but here is his story in brief.

Joseph Solomon Delmedigo was born in Candia on the Island of Crete in 1591, where his family was the island’s most prominent Jewish family. They were wealthy and intellectually gifted, and both Joseph’s father and grandfather served as rabbis. Joseph received a traditional Jewish education that was based on the study of Talmud as well as a general secular education, and he fondly remembered his early years: “ . . . From my youth the study of Talmud was like a father to me; all of my ancestors studied in yeshivot and later spread Torah learning and raised many disciples.”

He was sent to Padua to study medicine, and when he graduated he traveled to Lublin, Vilna, and Livona, where he spent much of his time working as a physician. He ultimately settled in Amsterdam where he published his Sefer Elim.

In this long book book Delmedigo outlined the reasons he accepted the Copernican model of the universe, and in so doing he became the first Jewish Copernican. In addition to explaining all of the theoretical support for the heliocentric model, he cited experimental evidence. If the planets revolved about the Sun and were illuminated by it, the amount of light that they reflect would depend on their location and distance from the Earth. And this is precisely what Delmedigo and his famous teacher had observed through the telescope. 

“Galileo my Teacher” from Delmedigo, Sefer Elim, Amsterdam 1629. 148.

My teacher Galileo observed Mars when it lay close to the Earth. At this time its light was much brighter than that of Jupiter, even though Mars is much smaller. Indeed it appeared too bright to view through the telescope. I requested to look through the telescope, and Mars appeared to me to be elongated rather than round. (This is a result of its clarity and the movement of its rays of light.) In contrast, I found Jupiter to be round and Saturn to be egg-shaped.

This glorious passage reminds us that religiously observant Jews were sometimes at the very cutting edge of the new astronomy. How many could claim to have been instructed by the great Galileo himself? And one other thing: unlike his contemporaries, Delmedigo described the telescope as an object of science, rather than as a means of teaching a spiritual lesson.

Chofetz Chaim Shem Olam. Warsaw 1895. Vol 1 p. 59.

Chofetz Chaim on the invention of the telescope

Much closer to our own times, Yisrael Meir (HaKohen) Kagan (1838 –1933) also used the telescope to make a spiritual point. Known popularly as the Chofetz Chaim, he was a giant of the last century. He authored the Mishnah Berurah, a widely used compendium of of Jewish law, as well as several books of ethics (mussar). It was in one of those works of mussar called Shem Olam that he made a connection between the invention of the telescope and the decline of religious observance. Its invention was a way to remind us of God’s providence in the world. Just as we can use the telescope to see high into the heavens, so too can God look down on us.

To understand properly the significance of the telescope, it is important to know that in the previous generation faith in providence was very strong. Everybody had perfect faith that even though God dwells above, nevertheless He supervises from His lofty abode all the inhabitants of the Earth… In that generation it was not necessary to have such things as telescopes.

However now, because of our many sins, we find many people who deny Providence and claim that God does not see or pay attention to what occurs in the world since He is so far away in Heaven. To counteract this false claim, God shows us clearly - by giving the inspiration to build the telescope - that even lowly man has the ability to see at the great distances from the Earth to the Heaven. So we realize that surely God has the ability to see from above to below concerning all matters… It follows from our discussion that all the scientific knowledge and technological advances that have occurred in our time - is not an indication that we are greater and more knowledgeable than previous generations. In fact it is only to validate for us the idea of Providence.

It is not clear to which generation the Chofetz Chaim was see referring. Was it that of Galileo, in whose era the telescope was perfected, or his own? And was Jewish observance in either of these times so much weaker than any other? In any event it is inconceivable that he was referring to the talmudic times of Rabban Gamliel, which means that the Chofetz Chaim was of the opinion that Rabban Gamliel’s tube could not have been the telescope as we know it.

AND A telescope named after a JEWISH FEMALE ASTRONOMER

Let’s end with a Jewish astronomer who just had an entire observatory named in her honor - Vera Rubin (1928-2016). She was born to Jewish immigrants in Philadelphia, educated at Vassar, Cornell and Georgetown, and moved to the Carnegie Institution in Washington in the 1960s. She studied the rotation of galaxies, and discovered that something other than their matter must be holding them together. As her obituary in The New York Times noted, “her work helped usher in a Copernican-scale change in cosmic consciousness, namely the realization that what astronomers always saw and thought was the universe is just the visible tip of a lumbering iceberg of mystery.” Being a woman in a man’s field had tremendous challenges, and called for ingenuity:

…she still had to battle for access to a 200-inch telescope on Palomar Mountain in California jointly owned by Carnegie and Caltech. When she did get there, she found that there was no women’s restroom. …Dr. Rubin taped an outline of a woman’s skirt to the image of a man on a restroom door, making it a ladies’ room.

Vera Rubin was elected to the National Academy of Sciences, and last year the Large Synoptic Survey Telescope was renamed the National Science Foundation Vera C. Rubin Observatory in recognition of her contributions to the study of dark matter and her outspoken advocacy for the equal treatment and representation of women in science. Dr Rubin now holds the distinction of being the Jew with the largest telescope named for her.

in conclusion

To sum, telescopes have served a number of different purposes for both rabbis and lay Jews.

• For Rabban Gamliel it was used as a measuring device, (though it likely wasn't a telescope at all).

• For Benjamin of Tudela is was a wondrous device to see for a distance of twenty days’ journey (though it was not a telescopes as we know them today, but some kind of mirror).

• For Azariah Figo it was a device that taught a religious lesson: just as physical weaknesses may be overcome with human ingenuity, so too might spiritual weaknesses be overcome.

• For Leon of Modena it was a proof of the greatness of Rabban Gamliel, who had used the device centuries before it was used in Europe.

• For Avraham Yagel, it was was a similar message: the rabbis of the Talmud had previously invented the telescope, long before it began to be used in Europe.

• For Joseph Delmedigo it was a scientific device that demonstrated the truth of the Copernican model.

• For the Chofetz Chaim its invention reminded us of God’s providence in the world. Just as we can use the telescope to see high into the heavens, so too can God look down on us.

• And for Vera Rubin, it was used as an object of honor for an extraordinary career.

NEXT TIME ON TALMUDOLOGY:

HOW RABBAN GAMLIEL USED TRIGONOMETRY

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[Many thanks to Dr. Howard Adelman from Queens University in Canada for his help in finding the original reference to Figo, and for pointing me to one about Leon of Modena.]